You can play as Shrek by typing "shrek" into chat (T to chat by default). He is large like Big da Cat, but is faster, has a smaller jump, and is Shrek. On the level Flame Core, there is a hidden Shrek statue located down a path to the left near the second to last checkpoint. The run would require you to complete every level as Shrek and visit the Shrek statue.

Thanks and may our ogrelord have mercy on your soul!

Edit: Corrections from Stuoid